Making a chain with changing size
All what is needed is an Array Modifiyer and an empty.



Add an array modifier to the oject. 
Add an empty to the scene at the red dot.
Scale and rotate the empty slightly. Thats to get a spiral and a decreasing size.



Adjust the fine tuning with the relative distance. (Y und X values in my case).



If the empty is rotated, it creats a chain ring.
If you want to print it: move the empty downwards, until all segments ar on the same hight.

Also there is an advantage because there is no curve modifier wich deformes the single sements of the chain.